Angular-resolved nonlinear optical response as a probe of Lorentz violation in noncentrosymmetric materials

We propose a methodology to detect weak Lorentz-violating (LV) backgrounds through the nonlinear shift photocurrent in noncentrosymmetric crystals. Using a spinful Rice--Mele model, we show that a LV background induces a momentum-odd correction to the Bloch Hamiltonian that reshapes the phase of the interband dipole matrix elements. As a result, the shift conductivity develops a robust $\pi$-periodic modulation as a function of the angle of a perpendicularly applied static electric field, in contrast to a weakly $2\pi$-periodic response of the Lorentz-symmetric case. This change in angular periodicity provides a signature of LV effects which can be directly identified through a photocurrent measurement. For realistic optical intensities, the predicted signal lies in the picoampere range, which can be enhanced in a matrix of weakly interacting chains, allowing sensitivity to LV coupling strengths of the order of $\xi\sim10^{-24}\,\mathrm{C\,m}$. These results establish nonlinear optical transport as a viable probe of emergent LV effects in solid-state systems.